Question

drag the tiles to the boxes to form correct pairs. not all tiles will be used. match the trinomials with their factors. factors: (a - 10)(a + 2), (a - 4)(a + 5), (a - 10)(a - 2), (a - 4)(a - 5) trinomials: $a^2 + a - 20$, $a^2 - 9a + 20$, $a^2 - 8a - 20$, $a^2 - 12a + 20$, $a^2 - 19a - 20$

Explanation:

Step1: Expand \((a - 4)(a + 5)\)

Using the distributive property \((x + y)(x + z)=x^2+(y + z)x+yz\), here \(x = a\), \(y=-4\), \(z = 5\). So \((a - 4)(a + 5)=a^2+(-4 + 5)a+(-4)\times5=a^2+a - 20\).

Step2: Expand \((a - 10)(a - 2)\)

Using the distributive property, \(x = a\), \(y=-10\), \(z=-2\). So \((a - 10)(a - 2)=a^2+(-10-2)a+(-10)\times(-2)=a^2-12a + 20\).

Step3: Expand \((a - 4)(a - 5)\)

Using the distributive property, \(x = a\), \(y=-4\), \(z=-5\). So \((a - 4)(a - 5)=a^2+(-4-5)a+(-4)\times(-5)=a^2-9a + 20\).

Step4: Expand \((a - 10)(a + 2)\)

Using the distributive property, \(x = a\), \(y=-10\), \(z = 2\). So \((a - 10)(a + 2)=a^2+(-10 + 2)a+(-10)\times2=a^2-8a - 20\).

Answer:

• \((a - 4)(a + 5)\) matches \(a^2 + a - 20\)
• \((a - 10)(a - 2)\) matches \(a^2 - 12a + 20\)
• \((a - 4)(a - 5)\) matches \(a^2 - 9a + 20\)
• \((a - 10)(a + 2)\) matches \(a^2 - 8a - 20\)